On portfolio management with value at risk and uncertain returns via an artificial neural network scheme

Abstract

This paper focuses on the computation issue of portfolio optimization with scenario-based Value-at-Risk. The main idea is to replace the portfolio selection models with linear programming problems. According to the convex optimization theory and some concepts of ordinary differential equations, a neural network model for solving linear programming problems is presented. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.